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AMSE JOURNALS –2015-Series: Modelling C; Vol. 70; N°1; pp15-28

Submitted Dec. 2014; Revised March 15, 2015; Accepted June 15, 2015

Direct Torque Control for Induction Motor with broken bars

using Fuzzy Logic Type-2

* S. Belhamdi, **A.Goléa

* Electrical Engineerng Lab. (LGE), University of M’sila, Algeria

**LGEB, University of Biskra, Algeria

(bsaad1@yahoo.fr)

Abstract: This paper introduces the design of a fuzzy logic controller in conjunction with direct

torque control strategy for induction motor machine. Fuzzy logic control is used to combine both

methods to obtain a compromise which reduces the sensitivity to the variation of the electrical

parameters (broken bars) at each operating point. The controller is designed according to fuzzy

logic rules, such that the system is fundamentally robust. To test the fuzzy control strategy a

simulation platform using MATLAB/SIMULINK was built which includes induction motor d-q

model, inverter model, fuzzy logic switching table and the stator flux and torque estimator. The

simulation results verified the new control strategy.

Keywords: Induction motor, DTC, type -2 Fuzzy logic, FL2DTC, Rotor fault.

1. Introduction

Advanced control of electrical machines requires an independent control of magnetic flux and

torque. For that reason it was not surprising, that the DC-machine played an important role in the

early days of high performance electrical drive systems, since the magnetic flux and torque are

easily controlled by the stator and rotor current, respectively. The introduction of Field Oriented

Control (Lascu, 2000) meant a huge turn in the field of electrical drives, since with this type of

control the robust induction machine can be controlled with a high performance. Later in the

eighties a new control method for induction machines was introduced (Vasudevan, 2005 and Lin

2007). The Direct Torque Control (DTC) method is characterized by its simple implementation

and a fast dynamic response. Furthermore, the inverter is directly controlled by the algorithm, i.e.

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a modulation technique for the inverter is not needed. However if the control is implemented on a

implemented on a digital system (which can be considered as a standard nowadays); the actual

values of flux and torque could cross their boundaries too far (Grawbowski, 2000), which is

based on an independent hysteresis control of flux and torque. The main advantages of DTC are

absence of coordinate transformation and cu Induction motor is widely used in industry because

of its reliability and low cost. However, since the dynamical model of induction motor is strongly

nonlinear, the control of induction motor is a challenging problem and has attracted much

attention. Many controllers have been developed. We can cite as follows.

FL was introduced by Zadeh in the 1960’s. FL is a superset of conventional (Boolean) logic that

has been extended to process data by allowing partial set membership rather than crisp set

membership or non-membership. FL is a problem-solving control system methodology. FL

provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise,

noisy, or missing input information.

Type-2 FLS have been developed that satisfy the following fundamental design requirement

(Mendel, 2001). When all sources of uncertainty disappear, a type-2 FLS must reduce to a

comparable type-1 FLS Takagi-Sugeno-Kang type fuzzy model structure, also being referred to

as TSK fuzzy logic systems (FLS) (Takagi & Sugeno, 1985), after Takagi, Sugeno & Kang, was

proposed in an effort to develop a systematic approach to generating fuzzy rules from a given

input-output data set. This model consists of rules with fuzzy antecedents and mathematical

function in the consequent part. Usually, conclusion function is in form of dynamic linear

equation. The antecedents divide the input space into a set of fuzzy regions, while consequents

describe behaviours of the system in those regions.

2. Direct Torque Control with Three-Level Inverter

The basic functional blocks used to implement the DTC scheme are represented in Figure 1. The

instantaneous values of the stator flux and torque are calculated from stator variable by using a

closed loop estimator (Grawbowski, 2000). Stator flux and torque can be controlled directly and

independently by properly selecting the inverter switching configuration (Vasudevan, 2005).

The voltage expressions of the machine used in the stator referential is given as:

rr

rrr

ssss

jwdt

dIRV

dt

dIRV

0

(1)

17

ReferanceFlux

-

-

Figure 1. Basic configuration of DTC scheme

2.1. Vector model of inverter output voltage

In a voltage fed three phases, the switching commands of each inverter leg are complementary.

So for each leg a logic state Si (C1, C2, C3) can be defined. Si is 1 if the upper switch is commanded

to be closed and 0 if the lower one in commanded to be close (first) (Lee, 2002).

Figure 2. Partition of the α β plane into 6 angular sectors

Since there are 3 independent legs there will be eight different states, so 8 different voltages.

Applying the vector transformation described as:

ReferanceTorque

Flux Stator

Torque

s

emT

IM

V0 …..V7

Ia Ib Ic

Stator flux and

Torque Estimator

Switching

State

Slector

α

β

1

6 5

4

3 2

600

18

3

4

3

2

3

2 j

cN

j

bNaNsss eVeVVjVVV

(2)

2.2. Stator flux control

The components of the current (Isα, Isβ), and stator voltage (Vsα, Vsβ) are obtained by the

application of the transformation given by (3) and (4), (Lee, 2002 and Vasudevan, 2005).

scsbs

sas

III

II

2

12

3

(3)

320

3210

2

12

1

2

3

CCUV

CCCUV

s

s

(4)

The components of the stator flux (ϕsα, ϕsβ) given by (5).

)()(

)()(

0

0

t

ssss

t

ssss

dtiRVt

dtiRVt

(5)

The electromagnetic couple be obtained starting from the estimated sizes of flux (ϕsα,ϕsβ and

calculated sizes of the current, Isα sβ .

).( ssssem IIpT

(6)

The stator resistance can be assumed constant during a large number of converter switching

periods Te. The voltage vector applied to the induction motor remains also constant during one

period Te. The stator flux is estimated by integrating the difference between the input voltage and

the voltage drop across the stator resistance as given by equations (7):

dtIRVt ssss (7)

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During the switching interval, each voltage vector is constant and (7) is then rewritten as in (8):

esss TVt 0

(8)

The angle of flux linkage θs an angle between stator’s flux and a reference axis is defined by

equation (9):

s

s

s

arctan

(9)

3. Fuzzy Logic Direct Torque Control of Induction Motor

In DTC induction motor drive, there are torque and flux ripples because none of the inverter

states is able to generate the exact voltage value required to make zero both the torque

electromagnetic error and the stator flux error (Belhamdi, 2013 and Saravana, 2009). The

suggested technique is based on applying switching state to the inverter and the selected active

state just enough time to achieve the torque and flux references values. A null state is selected for

the remaining switching period, which won't almost change both the torque and the flux.

Therefore, the switching state has to be determined based on the values of torque error, flux error

and stator flux angle. Exact value of stator flux angle (θs) determines where stator flux lies (Lee,

2002 and Ashok, 2009).

3.1. Type-2 Fuzzy Logic

A type-2 fuzzy set is characterized by a fuzzy membership function, where the

membership value or grade for each element of this set is a fuzzy set in the interval [0, 1]; unlike

a type-1 fuzzy set where the membership grade is a crisp value. As such, the membership

functions of type-2 fuzzy sets are three dimensional functions, with what is known as the set’s

footprint of uncertainty (FOU) representing the third dimension. In fact, it is this FOU that

provide type-2 FLSs with additional degrees of freedom and make it possible for them to directly

model and handle more types of uncertainties with higher magnitudes than their type-1

counterparts. Moreover, using type-2 fuzzy sets to represent a certain system’s inputs and outputs

can result in a smaller rule base as when a type-1 FLS was used. A block diagram of a typical

type-2 FLS is depicted in Figure. 2. It is generally composed of five components: a fuzzifier, a

rule base, a fuzzy inference engine, a type-reducer and a defuzzifier. In essence, it has a very

similar structure to a type-1 FLS (Wu, 2004 and Mendel, 2007).

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Type-2 fuzzy sets are generalized forms of those of type 1 (with the FOU as an additional degree

of freedom). Mathematically, a type-2 fuzzy set, denoted as A~

, is characterized by a type-2

membership function uxA

,~ , where Xx and 1,0 xJu

1,0,,,,~

~ xAJuXxuxuxA

(10)

In which 1,0 ~ uxA

.For a continuous universe of discourse,

A~

can be expressed as

1,0,

,~ ~

x

Xx Ju

A Jux

uxA

x

(11)

Where Jx is referred to as the primary membership of x. As in type-1 fuzzy logic, discrete fuzzy

sets are represented by the symbol instead of . The secondary membership function

associated to xx , for a given Xx , is the type-1 membership function defined by

xAJuuxx ,,~

(Qureshi,2009 and Mendel, 2007).

Figure 3. Block diagram of a type-2 FLS

The uncertainty in the primary membership of a type-2 fuzzy set A~

is represented by the FOU and

is illustrated in Figure.4. Note that the FOU is also the union of all primary memberships.

Xx

AFOU

)~

(

Reduced

sets

Fuzzifier

Defuzzifier

Rule Base

Inference

Type-2- output

Crisp

Inputs

x X

Type-reducer

Fuzzy sets x

Crisp

Type1

Fuzzy

Outputs y

Type-2-input

Fuzzy sets x

Output processing

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The upper and lower membership functions, denoted by xA~ and x

A~

, respectively, are two

type-1 membership functions that represent the upper and lower bounds for the footprint of

uncertainty of an interval type-2 membership function uxA

,~ , respectively FLS (Mendel,

2007). Membership function in interval type-2 fuzzy logic set as an area called Footprint of

Uncertainty (FOU) which is limited by two type1 membership function. Those are: Upper

membership Function (UMF) and Lower Membership function (LMF).

Interval type-2 membership function is shown in figure 4.

Figure.4. Interval type-2 fuzzy set with adjustable uncertain mean and adjustable standard

deviation.

Fuzzy logic type-2 system includes 4 components (Mendel, 2007):

Fuzzifier: Translates inputs (real values) to fuzzy values.

Inference System: Applies a fuzzy reasoning mechanism to obtain a fuzzy output.

Type Defuzzifier/Reducer: The defuzzifier translates one output to precise values; the

type reducer transforms a Type-2 Fuzzy Set into a Type-1 Fuzzy Set.

Knowledge Base: Contains a set of fuzzy rules, and a membership functions set known as

the database.

LMF

UMF

FOU

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Rule Control

It is assumed that the input data of the type-2 fuzzy system is x1 X1, x2 X2,………and

xp Xp , and fuzzy output sets is y Y . The rules of the type-2 fuzzy system are denoted as

follows: Ri: IF x1 is

ii

pp

ii GyFxFxF~

isthen~

isand.......~

isand~

221

xxFA

A

i

j ,~

Where denotes the jth antecedent of rule i and

iG~

indicates the

consequent of rule i.

The expert's experience is incorporated into a knowledge base with 25 rules (5 x 5). This

experience is synthesized by the choice of the input-output (I/O) membership functions and

the rule base. Then, in the second stage of the FLC, the inference engine, based on the input

fuzzy variables e and Δe, uses appropriate IF-THEN rules in the knowledge base to imply the

rules in the knowledge base to imply the final output fuzzy sets as shown in the Table1,

where NB, N, Z, P, PB, correspond to Negative Big, Negative, Zero, Positive, Positive Big

respectively (Belhamdi, 2013).

e

NB N Z P PB

NB NB NB N N Z

N NB N N Z PB

Δe Z N N Z P PB

P N Z P P PB

PB Z P P PB PB

Table1. Fuzzy rule for type-2 FLCs

4. Simulation Results

4.1. Healthy Case

Direct torque control of induction motor using fuzzy logic was also simulated using the

MATLAB / SIMULINK package. Membership functions were chosen and simulations were

carried out, the sampling time taken for simulation 4 s. Torque and flux reference values taken

were 3.5 N.m and 1.1 Wb. Figure (5) show the evolution the speed of the electromagnetic torque,

and stator current. Fine With of the mode of starting (0.2s). We observe that the control system

reaches its steady state by showing good performance and great stability for the two approaches.

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0 0.5 1 1.5 2 2.5 3 3.5 4-2

0

2

4

6

Time(s)

Ele

ctr

om

agnetic t

orq

ue(N

.m)

0 0.5 1 1.5 2 2.5 3 3.5 40

20

40

60

80

100

Time(s)

speed(r

ad/s

)

0 0.5 1 1.5 2 2.5 3 3.5 4-15

-10

-5

0

5

10

15

Time(s)

sta

tor

curr

ent(

A)

1 1.5 2 2.5 3 3.5 4-6

-4

-2

0

2

4

6

1 1.5 2 2.5 3 3.5 42.5

3

3.5

4

4.5

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

alpha axis flux

Beta

-axis

flu

x1 1.5 2 2.5 3 3.5 4

99.95

99.96

99.97

99.98

99.99

100

100.01

100.02

100.03

100.04

The flux and torque stabilize around their reference values. The simulation results show that flux

and torque responses are very good dynamic torque response for FLDTC2.

Fig. 5.e: The Stator current

Fig. 5.a: Speed response

Fig. 5.b: Zoom of speed response

Fig. 5.c: Torque for healthy motor

Fig. 5.f: Zoom of stator current

Figure. 5. Simulation results without Small-scale model

Fig. 5.d: The stator flux circle

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0 0.5 1 1.5 2 2.5 3 3.5 40

20

40

60

80

100

Time(s)

speed(r

ad/s

)

1 1.5 2 2.5 3 3.5 4

99.96

99.98

100

100.02

100.04

0 0.5 1 1.5 2 2.5 3 3.5 4-2

0

2

4

6

Time(s)

Ele

ctr

om

agnitic

torq

ue(N

.m)

1 1.5 2 2.5 3 3.5 42.5

3

3.5

4

4.5

4.2. Case of two broken bars

In the simulation tests a simplified mathematical model of the induction motor with broken

rotor bars was used .The each rotor fault was modeled as a full broken rotor bar. All simulation

tests were performed in per unit values .The squirrel-cage rotor of the tested IM consists of 16

bars .The reference speed is set to 100 rad/s (fig. 6. a). Then a load torque is applied at

t=0.8s.When the machine is healthy and when torque is required, symmetrical rotor-bar currents

appear with pulsation the slip frequency. At t=2s, we simulate a first bar is broken this is

achieved by increasing its resistance. We also note that the broken bar has no influence on the

dynamic responses of torque, speed, flux, and stator current. The second bar is broken a t=3s. We

notice the appearance of fluctuations on the shapes of the torque. Speed remains always not very

disturbed by this defect. For current I have one sees well a deformation during the rupture of the

bar. We can note that the broken bar does not affect the stability of system response. From this

analysis, the torque and flux present a high dynamic performances and good precision in steady

state. It can be observed that the torque and flux are decoupled.

Fig. 6.b: Zoom of speed response Fig. 6.a: Speed response

Fig. 6.c: Torque for healthy motor and broken

bar No 1 and 2 Fig. 6.d: Zoom for the torque

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0 0.5 1 1.5 2 2.5 3 3.5 4-15

-10

-5

0

5

10

15

Time(s)

Sta

tor

curr

ent(

A)

1 1.5 2 2.5 3 3.5 4-6

-4

-2

0

2

4

6

-1.5 -1 -0.5 0 0.5 1 1.5-1.5

-1

-0.5

0

0.5

1

1.5

alpha-axis flux

beta

- axis

flu

x

5. Conclusion

The main objective of this research was an analysis of the fault rotor influence on the FLDTC2

control signals and determining the visible absence of a signature in the selected control signals.

Simulation results show that FLDTC2 asynchronous machine can achieve precise control of the

stator flux and torque. Fuzzy Logic Direct Torque Control Type-2 an induction machine provides

a satisfactory solution to the problems of robustness and dynamics encountered in the control

technology based on the orientation of the rotor flux. Broken bar faults can have a significant

effect on the induction motor working operation. According to the results, the fault tolerant

Fig. 6.e: The Stator current Fig.6.f: Zoom of stator current

Fig. 6.g: The stator flux circle

Figure. 6. Simulation results without rotor defects

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control algorithm was confirmed effectively. Fault tolerant control in the induction is very

important to maintain system performance at an acceptable level. The algorithm used is very

effective and has been succeeded to maintain both speed and torque.

Appendix

Motors parameters (Belhamdi 2013)

Rs=7.58(Ω) Stator resistance

Rr=6.3(Ω) Rotor resistance

J=0.0054(Kgm2) Inertia

Ns=160 Number of turns per stator phase

Nr=16 Number of rotor bars

Rb=0.00015(Ω) Resistance of a rotor bar

Re=0.00015 (Ω) Resistance of end ring segment

Le=0.1e-6(H) Leakage inductance of end ring

Lb= 0.1e-6H Rotor bar inductance

p=2 Poles number

L=65(mm) Length of the rotor

E=25(mm) Air-gap mean diameter

L1s=0.0265(H) Mutual inductance

P=1.1(kW) Output power

K0=0 (SI) Friction coefficient

220/380(V) Stator voltage

50(Hz) Stator frequency

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